Some results on (a, d)-distance antimagic labeling
Abstract Let G = (V,E) be a graph of order N and f : V → {1, 2,...,N} be a bijection. For every vertex v of graph G, we define its weight w(v) as the sum ∑ u∈N(v) f(u), where N(v) denotes the open neighborhood of v. If the set of all vertex weights forms an arithmetic...
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| Autores principales: | , |
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| Lenguaje: | English |
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Universidad Católica del Norte, Departamento de Matemáticas
2020
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| Materias: | |
| Acceso en línea: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172020000200361 |
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| Sumario: | Abstract Let G = (V,E) be a graph of order N and f : V → {1, 2,...,N} be a bijection. For every vertex v of graph G, we define its weight w(v) as the sum ∑ u∈N(v) f(u), where N(v) denotes the open neighborhood of v. If the set of all vertex weights forms an arithmetic progression {a, a + d, a + 2d, . . . , a + (N − 1)d}, then f is called an (a, d)-distance antimagic labeling and the graph G is called (a, d)-distance antimagic graph. In this paper we prove the existence or non-existence of (a, d)- distance antimagic labeling of some well-known graphs. |
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